If a square matrix A satisfies 4 – 24 – 71 = 0, which of the following is equal to A1? A) (81+ 4²) (B) (21+4P) (C)}(81-&²) D)-71 + 4²) E)-(1-A²) (І2I-A³ ) G) - (31+ 4²) (H)-(21– 4²)

Q: [2 8) Use the Gauss-Jordan method to find the inverse of the matrix A: %3D

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A: The given statement is

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Q: Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

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Q: If A * I = A, and A is a 3x5 matrix, what are the dimensions of I? Show complete solution as proof.

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Q: Suppose that A−1 and the LU factorization of A have already been determined. How many scalar…

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Q: 4 6 , calculate A by using Adjoint Matrix Method. (Do not use any other method) 3 5 2 ) For A =

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Q: Show that a square matrix which has a row or a column consisting entirely of zeros must be singular.

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Q: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

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Q: 2) An n x n matrix A is called nilpotent if Ak = 0 for some positive integer k. Show that if A + 0…

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Q: Let A be 7×9 matrix. Knowing that Rank (A) 3. Then Nullity(A) is equal to: ||

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Q: A and B are 3,3 matrices. Lo lAl =-3 and IBl =2. SO phat is l-2A02|?

A: Properties of determinant:kA=knAAB=ABA-1=1A

Q: 2 -3 -2 3 1 2 -2 -1 3 3 [ 3 2 -2

A: The given matrix is  A=  2-3-2   3  1   2-2   0-1   3   3   2   3   2   2-2

Q: Construct 3×2 matrices A and B so that Ax​=0 has only the trivial​ solution, but Bx​=0 has…

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Q: 2 Prove that the 3 × 3 matrix A = 4 -1 cannot be factored as A = LDL". 1 -1 3

A: In the question it is asked to show that the matrix A=12124-11-13 cannot be factored as A=LDLT.

Q: 8.) If A is an mxn matrix, what are the largest possible value for its rank and the smallest…

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A: Please check step 2 for the solution.

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Q: Suppose A is a 4 × 4 coefficient matrix. If possible, find the entries of a matrix T that perform…

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Q: Could a rref matrix look like | 1 0 0 1 | | 0 1 0 1…

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Q: Show that if a 3×3 matrix A is never sad then the entries along its diagonal, i.e. a11, a22, a33,…

A: Let 3×3 matrix A is never sad

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Q: Го 7 [4 Suppose a matrix A is row-equivalent to the matrix 6 11 47 For the vector b = 2 performing…

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Q: 2. Construct a 4x4 nonzero matrix A such that the vector -3 is a solution of Ax= 0. -4 2.

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Q: When a matrix is multiplied by a scalar k, then every entry of the matrix is multiplied by k.  True…

A: It is TRUE by definition which is given below.

Q: 5. Solve Ax by forming an augmented matrix and using Gauss Jordan Elimination = a

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Q: Find matrix K such that MKN = O if Show complete solution. 1 M = -2 3 1 2 0 0 1 N= 0 8 6 6-1 -4 0 -2…

A: Given- M=14-231-2N=20001-1O=86-66-11-400 To find- K such that MKN=0

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Q: Find an upper triangular matrix that satisfies 18 -8 0

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Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

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Q: 2. By using Hadamard matrices of order 2 and 4, construct a Hadamard matrix of order 8.

A: Given: Let us construct a Hadamard matrix of order 8 using the Hadamard matrices of orders 2 and 4.

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A: We will give a counter example that will prove this statement wrong.

Q: Find a 2 × 1 matrix x with entries not all zero such that

A: Given: Ax=3x, where A=2112 let's assume matrix x is x=ab

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Q: Let A be 3x5 matrix. Then AX=b has always infinitly many solutions.

A: Let A be 3×5 matrix . The matrix equation is: AX = b; where A is the coefficient matrix, X is the…

Q: Suppose that a l10 × 8 matrix A has 6 pivot columns. Then dim(ColA)- is Ą and dim(RowA)- is

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Q: 5. Show that if M is a 3 x 3 magic square with weight w, then we can write M as M = Mo+ kJ where Mo…

A: M is a 3 x 3 magic square matrix with weight w. We take weight, w=15 The matrix of M is  Add any…

Q: Suppose A is a 4 × 4 coefficient matrix If possible, find the entries of a matrix T that perform the…

A: Given that A is a 4×4 co-efficient matrix.We have to find T (matrix), whereA→(3R4+R4)AT, which means…

Q: Suppose that A is a 18 × 14 matrix that has 10 pivot columns. Then: (1) dim(ColA) is (i) dim(RowA)…

A: NOTE: Refresh your page if you can't see any equations. . the dimension of the matrix is  which the…